Highest Common Factor of 167, 472, 915, 660 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 167, 472, 915, 660 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 167, 472, 915, 660 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 167, 472, 915, 660 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 167, 472, 915, 660 is 1.
HCF(167, 472, 915, 660) = 1
HCF of 167, 472, 915, 660 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 167, 472, 915, 660 is 1.
Highest Common Factor of 167,472,915,660 is 1
Step 1: Since 472 > 167, we apply the division lemma to 472 and 167, to get
472 = 167 x 2 + 138
Step 2: Since the reminder 167 ≠ 0, we apply division lemma to 138 and 167, to get
167 = 138 x 1 + 29
Step 3: We consider the new divisor 138 and the new remainder 29, and apply the division lemma to get
138 = 29 x 4 + 22
We consider the new divisor 29 and the new remainder 22,and apply the division lemma to get
29 = 22 x 1 + 7
We consider the new divisor 22 and the new remainder 7,and apply the division lemma to get
22 = 7 x 3 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 167 and 472 is 1
Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(29,22) = HCF(138,29) = HCF(167,138) = HCF(472,167) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 915 > 1, we apply the division lemma to 915 and 1, to get
915 = 1 x 915 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 915 is 1
Notice that 1 = HCF(915,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 660 > 1, we apply the division lemma to 660 and 1, to get
660 = 1 x 660 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 660 is 1
Notice that 1 = HCF(660,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 167, 472, 915, 660 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 167, 472, 915, 660?
Answer: HCF of 167, 472, 915, 660 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 167, 472, 915, 660 using Euclid's Algorithm?
Answer: For arbitrary numbers 167, 472, 915, 660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
